Explain sampling frames and units

Questions asking students to suggest or define sampling frames, identify sampling units, or explain advantages/disadvantages of samples versus census.

8 questions

Edexcel S2 2024 June Q3
3 Jian owns a large group of shops. She decides to visit a random sample of the shops to check if the stocktaking system is being used incorrectly.
  1. Suggest a suitable sampling frame for Jian to use.
  2. Identify the sampling units.
  3. Give one advantage and one disadvantage of taking a sample rather than a census. Jian believes that the stocktaking system is being used incorrectly in \(40 \%\) of the shops.
    To investigate her belief, a random sample of 30 of the shops is taken.
  4. Using a 5\% level of significance, find the critical region for a two-tailed test of Jian’s belief.
    You should state the probability in each tail, which should each be as close as possible to 2.5\% The total number of shops, in the sample of 30, where the stocktaking system is being used incorrectly is 20
  5. Using the critical region from part (d), state what this suggests about Jian’s belief. Give a reason for your answer. Jian introduces a new, simpler, stocktaking system to all the shops.
    She takes a random sample of 150 shops and finds that in 47 of these shops the new stocktaking system is being used incorrectly.
  6. Using a suitable approximation, test, at the \(5 \%\) level of significance, whether or not there is evidence that the proportion of shops where the stocktaking system is being used incorrectly is now less than 0.4 You should state your hypotheses and show your working clearly.
Edexcel S2 2004 January Q1
  1. A large dental practice wishes to investigate the level of satisfaction of its patients.
    1. Suggest a suitable sampling frame for the investigation.
    2. Identify the sampling units.
    3. State one advantage and one disadvantage of using a sample survey rather than a census.
    4. Suggest a problem that might arise with the sampling frame when selecting patients.
    5. The random variable \(R\) has the binomial distribution \(\mathrm { B } ( 12,0.35 )\).
    6. Find \(\mathrm { P } ( R \geq 4 )\).
    The random variable \(S\) has the Poisson distribution with mean 2.71.
  2. Find \(\mathrm { P } ( S \leq 1 )\). The random variable \(T\) has the normal distribution \(\mathrm { N } \left( 25,5 ^ { 2 } \right)\).
  3. Find \(\mathrm { P } ( T \leq 18 )\).
Edexcel S2 2002 June Q1
\begin{enumerate} \item The manager of a leisure club is considering a change to the club rules. The club has a large membership and the manager wants to take the views of the members into consideration before deciding whether or not to make the change.
  1. Explain briefly why the manager might prefer to use a sample survey rather than a census to obtain the views.
  2. Suggest a suitable sampling frame.
  3. Identify the sampling units. \item A random sample \(X _ { 1 } , X _ { 2 } , \ldots , X _ { n }\) is taken from a finite population. A statistic \(Y\) is based on this sample.
Edexcel S2 Q1
  1. (a) Explain why it is often useful to take samples as a means of obtaining information.
    (b) Briefly define the term sampling frame.
    (c) Suggest a suitable sampling frame for a sample survey on a proposal to install speed humps on a road.
  2. An insurance company conducts its business by using a Call Centre. The average number of calls per minute is \(3 \cdot 5\). In the first minute after a TV advertisement is shown, the number of calls received is 7 .
    (a) Stating your hypotheses carefully, and working at the \(5 \%\) significance level, test whether the advertisement has had an effect.
    (b) Find the number of calls that would be required in the first minute for the null hypothesis to be rejected at the \(0.1 \%\) significance level.
  3. On average, \(35 \%\) of the candidates in a certain subject get an A or B grade in their exam. In a class of 20 students, find the probability that
    (a) less than 5 get A or B grades,
    (b) exactly 8 get A or B grades.
Five such classes of 20 students are combined to sit the exam.
(c) Use a suitable approximation to find the probability that less than a quarter of the total get A or B grades.
Edexcel S2 Q1
  1. (a) Briefly explain the difference between a one-tailed test and a two-tailed test.
    (b) State, with a reason, which type of test would be more appropriate to test the claim that this decade's average temperature is greater than the last decade's.
  2. (a) Give one advantage and one disadvantage of
    1. a sample survey,
    2. a census.
      (b) Suggest a situation in which each could be used.
    3. A pharmaceutical company produces an ointment for earache that, in \(80 \%\) of cases, relieves pain within 6 hours. A new drug is tried out on a sample of 25 people with earache, and 24 of them get better within 6 hours.
      (a) Test, at the \(5 \%\) significance level, the claim that the new treatment is better than the old one. State your hypotheses carefully.
    A rival company suggests that the sample does not give a conclusive result;
    (b) Might they be right, and how could a more conclusive statement be achieved?
Edexcel S2 Q1
  1. Briefly explain what is meant by
    1. a statistical model,
      (2 marks)
    2. a sampling frame,
    3. a sampling unit.
    4. (a) Explain what is meant by the critical region of a statistical test.
    5. Under a hypothesis \(\mathrm { H } _ { 0 }\), an event \(A\) can happen with probability \(4 \cdot 2 \%\). The event \(A\) does then happen. State, with justification, whether \(\mathrm { H } _ { 0 }\) should be accepted or rejected at the \(5 \%\) significance level.
Edexcel S2 Q1
  1. (a) State one advantage and one disadvantage in using a census rather than a sample survey in statistical work.
    (b) Give an example of a situation in which you would choose to use a census rather than a sample survey and explain why.
    (2 marks)
  2. An advert for Tatty's Crisps claims that 1 in 10 bags contain a free scratchcard game.
Tatty's Crisps can be bought in a Family Pack containing 10 bags. Find the probability that the bags in one of these Family Packs contain
(a) no scratchcards,
(b) more than 2 scratchcards. Tatty's Crisps can also be bought wholesale in boxes containing 50 bags. A pub Landlord notices that her customers only found 2 scratchcards in the crisps from one of these boxes.
(c) Stating your hypotheses clearly, test at the \(10 \%\) level of significance whether or not this gives evidence of there being fewer free scratchcards than is claimed by the advert.
(4 marks)
Edexcel S2 Q2
2. A driving instructor keeps records of all the learners she has taught. In order to analyse her success rate she wishes to take a random sample of 120 of these learners.
  1. Suggest a suitable sampling frame and identify the sampling units. She believes that only 1 in 20 of the people she teaches fail to pass their test in their first two attempts. She decides to use her sample to test whether or not the proportion is different from this.
  2. Using a suitable approximation and stating clearly the hypotheses she should use, find the largest critical region for this test such that the probability in each "tail" is less than \(2.5 \%\).
  3. State the significance level of this test.